Question

A printer will produce 80 wedding invitations for $210. The price to produce 120 invitations is $290. The printer uses a linear function to determine the price for producing different amounts of invitations. How much will the printer charge to produce 60 invitations?

A)$120.00
B)$145.00
C)$157.50
D)$170.00

Answer 1

The printer charge is $170 to produce 60 invitations.

Explanation:

A printer will produce 80 wedding invitations for $210

`(x_1,y_1)=(80,210)`

The price to produce 120 invitations is $290.

`(x_2,y_2)=(120,290)`

We will use two point slope form

Formula :
`y- y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values :

`y- 210=(290-210)/(120-80)(x-80)`

`y- 210=2(x-80)`

`y- 210=2x-160`

`y- 210=2x-160`

`y=2x+50`

Now we are supposed to find the printer charge to produce 60 invitations

Substitute x = 60

`y=2(60)+50`

`y=170`

Hence the printer charge is $170 to produce 60 invitations.

Answer 2

Answer: Option 'D' is correct.

Explanation:

Let the number of wedding invitations be represented by x axis.

Let the cost of wedding invitations be represented by y-axis.

So, At cost of $210, a printer will produce 80 wedding invitations.

At cost of $290, a printer will produce 120 wedding invitations.

So, we have (80,210) and (120,290)

So, our equation of slope will become:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\y-210=(290-210)/(120-80)(x-80)\\\\y-210=(80)/(40)(x-80)\\\\y-210=2(x-80)\\\\y-210=2x-160\\\\y=2x-160+210\\\\y=2x+50`

We need to find the cost of 60 (= x) invitations:

`y=2x+50\\\\y=2* 60+50\\\\y=120+50\\\\y=\$170`

Hence, Option 'D' is correct.